Abstract
The paper deals with measuring change based on observed frequencies of certain critical events. On the assumption that (i) a “specifically objective” probabilistic assessment of change in event frequencies be possible which (ii) rests on the conditional likelihood function of observed events, given the total number of such events, it is shown that the event frequencies must be governed by a multiplicative “power series model” (PSM). If, in addition, unobserved events prior to the beginning of a defined observation epoch may be ignored (“ignorability assumption”), then the model must be a multiplicative Poisson model (MPM) as a special case of a PSM. Basic properties of the PSM and the MPM are investigated, an efficient method for parameter estimation and hypothesis testing in the MPM is presented, and its use is demonstrated by means of a sample application from clinical psychology. Finally, a quite different interpretation of the PSM as a rating scale model is mentioned.
The author is indebted to Immanuel Bomze, Department of Statistics, University of Vienna, and to anonymous reviewers for valuable comments on a previous draft of this paper, and to Brigitte Wild for the MPM estimation program.
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References
Andersen, E. B. (1980). Discrete statistical models with social science applications. Amsterdam: North-Holland.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.
Barndorff-Nielsen, O. (1978). Information and exponential families in statistical theory. New York: Wiley.
Feller, W. (19683). An introduction to probability theory and its applications (Vol. 1). New York: Wiley.
Fischer, G. H. (1977). Some probabilistic models for the description of attitudinal and behavioral changes under the influence of mass communication. In W. F. Kempf & B. H. Repp (Eds.), Mathematical models for social psychology. Berne: Huber, 102–151.
Fischer, G. H. (1987). Applying the principles of specific objectivity and of generalizability to the measurement of change. Psychometrika, 52, 565–587.
Fischer, G. H. (1989). An IRT-based model for dichotomous longitudinal data. Psychometrika, 54, 599–624.
Fischer, G. H. & Parzer, P. (1989). An extension of the rating scale model with an application to the measurement of change. Paper presented at the Sixth Workshop on Item Response Theory, October 10–12, 1989, University of Twente, Enschede (submitted).
Galambos, J. & Kotz, S. (1978). Characterizations of probability distributions. Berlin: Springer.
Haight, F. A. (1967). Handbook of the Poisson distribution. New York: Wiley.
Huber, H. P., Huber, D., & Hunger, J. (1985). Zur nicht-medikamentösen Behandlung der Migräne: Eine vergleichende Therapiestudie. In H.-U. Wittchen & J. C. Brengelmann (Eds.), Psychologische Therapie bei chronischen Schmerzpatienten. Berlin: Springer, 5–22.
Johnson, N. L. & Kotz, S. (1969). Distributions in statistics: Discrete distributions. Boston: Houghton Mifflin.
Little, R. J. A. & Rubin, D. R. (1987). Statistical analysis with missing data. New York: Wiley.
McCullagh, P. & Neider, J. A. (1983). Generalized linear models. London: Chapman and Hall.
Noack, A. (1950). A class of random variables with discrete distributions. Annals of Mathematical Statistics, 21, 127–132.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Pædagogiske Institut.
Rasch, G. (1967). An informal report on a theory of objectivity in comparisons. In L. J. Th. van der Kamp & C. A. J. Vlek (Eds.), Measurement theory. Proceedings of the NUFFIC international summer session in science at “Het Oude Hof”. The Hague, July 14–28, 1966. Leyden: University of Leyden.
Rasch, G. (1968). A mathematical theory of objectivity and its consequences for model construction. Paper presented at the European Meeting on Statistics, Econometrics and Management Science, Amsterdam.
Rasch, G. (1972). Objectivitet i samfundsvidenskaberne et metodeproblem. (Objectivity in the social sciences as a methodological problem.) Nationalßkonomisk Tidsskrift, 110, 161–196.
Rasch, G. (1977). On specific objectivity: An attempt at formalizing the request for generality and validity of scientific statements: In M. Blegvad (Ed.), The Danish yearbook of philosophy. Copenhagen: Munksgaard.
Rubin, D. R. (1976). Inference and missing data. Biometrika, 63, 581–590.
Scheiblechner, H. (1972). Personality and system influences on behavior in groups: Frequency models. Acta Psychologica, 36, 322–336.
Wright, B. D. & Masters, G. N. (1982). Rating scale analysis. Chicago: Mesa Press.
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Fischer, G.H. (1991). On Power Series Models and the Specifically Objective Assessment of Change in Event Frequencies. In: Doignon, JP., Falmagne, JC. (eds) Mathematical Psychology. Recent Research in Psychology. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9728-1_17
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DOI: https://doi.org/10.1007/978-1-4613-9728-1_17
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